What makes you randomly diagnose that as the problem, do loose bluetooth modules cause black screens? I thought they just made it so you wouldnt be able to connect your Wiimote. Anyway we need more details regarding his system before making baseless assumptions like a busted bluetooth module. Throwing out suggestions without putting any thought into it will only leave the OP more confused, and may send him on time wasting tangents when all he needed was something simple.

Loose bluetooth models do, in fact, cause a black screen. It's a very well known issue, and searching the board should bring up plenty of topics mentioning that. Maybe you should do some research before calling people out on it?

As for the OP, if the GCN savemii trick doesn't work, neither will the dongle. So don't bother buying it. I have a feeling you don't really know what it is or how it works anyway so it's just wasted money if you go through with it.

It is not the BT module, savemiifrii would work if it was. BT module going bad is pretty common, so it is a good place to start, but RM will load via savemii/savemiifrii so this is not the issue.

@OP if this brick is random and has not resolved, it could possible by a bad wifi module (rare), or even a very bad dvd drive (very rare).
If you did not do anything to brick your wii you can test this.
-You can test the wifi by swaping it with a working one
-You can test the dvd drive by simply unplugging it.